MOSCOW—When it opened in 1990, the McDonald's on Moscow's Pushkin Square was a symbol of thawing relations with the U.S., attracting long lines and later becoming the fast-food chain's most visited outlet world-wide.

On Wednesday evening, it stood empty, closed by Russia's consumer-safety regulator amid the Kremlin's most serious confrontation with the West since the Cold War. The agency cited sanitary violations as it said that it...